Semisupervised Sparse Manifold Discriminative Analysis for Feature Extraction of Hyperspectral Images

The graph embedding (GE) framework is very useful to extract the discriminative features of hyperspectral images (HSIs) for classification. However, a major challenge of GE is how to select a proper neighborhood size for graph construction. To overcome this drawback, a new semisupervised discriminative learning algorithm, which is called the semisupervised sparse manifold discriminative analysis (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> MDA) method, was proposed by using manifold-based sparse representation (MSR) and GE. The proposed algorithm utilizes MSR to obtain the sparse coefficients of labeled and unlabeled samples. Then, it constructs a within-class graph and a between-class graph using the sparse coefficients of labeled samples, as well as an unsupervised graph with the sparse coefficients of unlabeled samples. Finally, it uses these graphs to obtain a projection matrix for feature extraction (FE) of HSI in a low-dimensional space. The S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> MDA method not only inherits the merits of MSR to reveal the sparse manifold properties of data but also enhances interclass separability and intraclass compactness to improve the discriminating power for classification. Extensive experiments on two real HSI data sets obtained with a reflective optics system imaging spectrometer and an airborne visible/infrared imaging spectrometer show that the proposed algorithm is significantly superior to other state-of-the-art FE methods in terms of classification accuracy.